Accession Number:

AD0701156

Title:

CONVEXITY PRESERVING SCALE TRANSFORMATIONS,

Descriptive Note:

Corporate Author:

BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s):

• Marshall,Albert W.
• Proschan,Frank

Report Date:

1969-12-01

Pagination or Media Count:

18.0

Abstract:

Let C be the class of increasing convex functions on the interval from zero to but less than infinity with f0 0. Then f epsilon C implies that the composition psifpsi superscript-1 epsilon C if and only if psix cx to the power p, c 0, p or 1. Functions psi for which psifpsi superscript-1 epsilon C whenever f epsilon C are characterized for various other classes C, e.g., the concave, starshaped or superadditive increasing functions f on the interval from zero to but less than infinity with f0 0. In addition, classes of functions on other domains, and logarithmically convex or concave functions are also considered. Author

Descriptors:

• (*FUNCTIONS(MATHEMATICS)
• *TRANSFORMATIONS(MATHEMATICS))
• RELIABILITY
• SET THEORY
• THEOREMS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE